You didn't note what the amp hours of the battery are. Without all the figures, it's not possible to determine if the freezer will ever work on the smallish solar system you have.
Also just because the controller showed 13.7 while the solar was working is no indication of whether you got the battery to a full charge. That would depend on the state of the battery before you hooked up solar, how long the solar was active and how much power was being pulled from the battery at the same time as you were using the solar.
I run a 65 Qt Whynter as a freezer as well as another unit the same size as a fridge. The freezer takes 4 to 5 times the power to keep it as 0 F as it does to keep the fridge at 40F. I run the pair on 4 - 6 volt Trojan T105RE batteries and use the generators on a regular basis to ensure that my batteries are kept well charged since I have chosen to only have 200 Watts of solar for use in the sunny southern clime in winter.
The Whynter has a low voltage shut off built in. If there's not enough power in the battery, the unit shuts off, waits a while to see if you're applying power and tries again.
Oh crap I just realized you're using your starting battery to try to power the freezer....I really wouldn't try that IIWM. You'll most likely be causing that starting battery to get to the point where your vehicle won't start. Do that a few times and you'll be replacing that battery.